Last week we introduced our new grade nine math practice section and talked about quadratic equations and their practical application. We also mentioned the importance they play in future mathematical processes, but this week we want to focus on the next section in Grade nine, namely circles. In this blog we mentioned shapes and circles briefly; however, we didn’t talk too much about the properties of circles. That is something incorporated into our grade nine section directly after quadratics. These two topics are extremely important in the mathematical world because they have intrigued (and sometimes baffled) people for centuries.
A circle is so simple to look at, but our ways of measuring them are never exact. That is, we use the irrational number Pi to help us estimate dimensions of circles. We know that given the radius of any circle we can calculate its circumference by multiplying two by Pi and the radius, but since Pi isn’t an exact number we will never get the true circumference. We can use computer programs to calculate Pi to millions (probably trillions) of decimal places, giving us an almost perfect value, but never truly perfect; fascinating. The infinity of Pi is hard to imagine because circles look so simple, but when we examine them closely it’s easy to see why they can’t ever be accurately measures; they will have microscopic imperfections. The current world record for a human memorizing Pi is set at 67.890 decimal places and it took him over 24 hours to recite, something they would have to do in one sitting (not an easy feat!).
Computers have helped us understand mathematics and other elements in our universe, such as astrophysics. There are things that can be easily taught using computer programs, such as BeijingMath, that aren’t so easy to understand without one. With our grade nine section on circles we try to give students a unique understanding of the principles governing them, hopefully making them easier to understand. There are certain aspects of circles that are constant, such as the radius and diameter, but that also allows us to determine other aspects of the circle, such as the circumference and area. Of course, these are basic examples when it comes to circles and our section in grade nine delves far deeper into the fundamentals of circle properties, such as secants and tangents. We start be examining these closely and progress to other polygons, teaching children how to understand angles in certain shapes.
In the last section on circles we work on arcs, chords and sectors and this will give students an excellent grasp of circle and polygon theory. Once a student has mastered quadratics and circle concepts it will make future math sections a lot easier to comprehend, but that doesn’t mean it will make them easy! Math is a complicated subject and one that nobody truly understands completely, as noted in our blog with the Goldbach Conjecture.